Quantum-Classical Correspondence Principle for Heat Distribution in Quantum Brownian Motion.

Area of Science:

• Quantum thermodynamics
• Quantum statistical mechanics
• Condensed matter physics

Background:

• The Caldeira-Leggett model describes quantum Brownian motion, crucial for understanding quantum thermodynamics.
• Classical thermodynamics concepts like work and heat are being explored in quantum regimes.
• Phase-space formulations offer a powerful tool for analyzing quantum systems.

Purpose of the Study:

• To investigate the heat distribution during relaxation in a quantum Brownian motion model.
• To derive analytical results for the characteristic function of heat.
• To establish quantum-classical correspondence for heat distribution and verify fluctuation theorems.

Main Methods:

• Utilizing the phase-space formulation approach.
• Analyzing the Caldeira-Leggett model for quantum Brownian motion.
• Deriving the characteristic function of heat for arbitrary relaxation times and friction coefficients.

Main Results:

• An analytical result for the characteristic function of heat was obtained for quantum Brownian motion.
• The classical limit of the derived heat distribution matches that of classical Brownian motion (Langevin equation).
• Demonstrated that fluctuating heat satisfies the exchange fluctuation theorem and shows complete thermalization.

Conclusions:

• The study provides a quantum-classical correspondence for heat distribution.
• The definition of quantum fluctuating heat is justified through two-point measurements.
• The findings contribute to a deeper understanding of quantum thermodynamics and thermalization processes.